Dispersion relations are derived to determine the growth rate, dominant wavelength, and group velocity of disturbances caused by the beam breakup instability. Considerations include weak and strong focusing, x-y coupling in solenoidal transport, the spacing of accelerator cavities, and periodically pulsed beams. Beam breakup growth is minimum when the cavity spacing equals an integral number of...

We discuss self-similar solutions for jet breakup for a family of models of nonNewtonian fluids which includes the Phan-Thien Tanner model. The constitutive law is given by Tt + (v · ∇)T− (∇v)T−T(∇v)T + κT +ν(trT)a−1T = μ(∇v + (∇v)T ), (1) where a > 1. For a = 2, a recent paper establishes the existence of a similarity solution for surface tension driven jet breakup. In this paper, we show that...

We discuss the quasi-adiabatic approximations to the three-body wavefunction in breakup processes, clarifying the assumptions underlying the model. This suggests alternative approximation schemes. Using different theoretical three-body models, calculated differential cross section angular distributions for the Be(p,d) reaction, for which new preliminary data have been reported at 35 MeV, are pr...

We present a practical method to solve Faddeev three-body equations at energies above three-body breakup threshold as integral equations in coordinate space. This is an extension of previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels...

Considering markets with nonpivotal buyers, we analyze the anticompetitive effects of breakup fees used by an incumbent facing a more efficient entrant in the future. Buyers differ in their intrinsic switching costs. Breakup fees are profitably used to foreclose entry, regardless of the entrant’s efficiency advantage or level of switching costs. Banning breakup fees is beneficial to consumers. ...

An analytic theory of cumulative multibunch beam breakup in linear colliders is developed. Included is a linear variation of transverse focusing across the bunch train as might be applied, e.g., by chirping the radiofrequency power sources or by using radiofrequency quadrupole magnets. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic decay...

Numerical simulations are conducted to investigate the primary atomization of a round liquid jet surrounded by a coaxial flow of gas. A Refined Level Set Grid (RLSG) method coupled to a Lagrangian spray model is used to capture the whole breakup process of the liquid jet. In the near field of the liquid jet, where the primary breakup occurs, motion and topological changes of the liquid jet are ...

The breakup of droplets in an inhomogeneous flow is the key to emulsification. Frequently, the local flow experienced by the drops is a (quasi-) simple shear flow. The breakup of droplets in a steady, simple shear flow in the absence of emulsifiers has been studied extensively. In the presence of emulsifiers, the droplet interface may acquire viscoelastic properties, which are important in the ...

Due to the high content of cellulose, hemicellulose and lignin, the anisotropy of biomass particle in spatial structure induces the difference of mechanical properties in different directions. In this paper, based on the finite stochastic breakup model and anisotropy of biomass particles, 2-dimensional finite stochastic breakup model (2D-FSBM) of biomass particle was proposed, and the breakup p...

The steady deformation and breakup of emulsion drops in a uniform electric field are considered experimentally. Due to the low volume fraction of inner drops, the emulsions can be effectively assumed as Newtonian fluids with spatial nonuniformity. The measurements of the electrical properties show that the oil-in-water (o/w) emulsion drop behaves like a conducting drop. On the other hand, the w...